linking elastic, mechanical and transport properties in ... · transport properties of cracked...

Eurorock Conference, Erice, Italy, 25-30 Sept. 2007 2007

Linking elastic, mechanical and transport properties in(thermally) cracked rocks

Alexandre Schubnel, M.H.B. Nasseri, Phil Benson, Phil Meredith, R.Paul Youngand Yves Gueguen


Context

Cracks:

In crustal conditions, all rocks contain cracks, which, although representing anextremely small amount of porosity, have been identified for a long time as a majorcause of elastic properties variations (Walsh 1965; Simmons and Brace1965),mechanical strength reduction and preferred conduits for fluid flow.

E.g. their existence can explain the differences observed between static anddynamic elastic moduli, part of the elastic anisotropy of rocks (all of it when nopreferred CPO, Kern 1978). They also enhance the rock connectivity to fluid (~φ3),and thus electric conductivity for instance, etc.

Cracks are very compliant and may propagate (consequences on length, apertureand roughness). And are generally saturated with fluids (water, CO2, magma,oil, gas, etc…)

Aligned crack pattern in Takadeni granite, Benson et al., 2006


Motivation

1. Understand the spatio-temporal evolutiono f e l a s t i c p r o p e r t i e s i n t e r m s o fp o r o s i t y / d a m a g e / s a t u r a t i o n

2. U n d e r s t a n d t h e c o u p l i n g a n d / o rdecoupling between the evolutions ofporosity/ damage/ elastic wave velocitiesa n d f l u i d f l o w ( p e r m e a b i l i t y )

3. Predict the evolution of damage - andpermeability - what we would like to knowin reservoirs, geothermal areas, faultzones, vo lcan ic areas e tc . f rom theevolution of elastic wave velocities (whatw e c a n “ e a s i l y ” m e a s u r e )

P wave tomography in the Rift of Assal (Ethiopia), from Doubre et al., [2002]


Physical properties of cracked rocks with thermal treatment: experimentalmeasurements

stress field:Isotropic ~ burial σ1=σ3+ Pore pressure Pp

Application to a Heat treated (RT, 250, 450, 650 & 850 deg C, isotropic granite (Westerly)


Physical properties of cracked rocks with thermal treatment:Link with microstructureEvolution of crack density patterns in heat treated Westerly. G., from Nasseri et al., IJRM, 2007


Mechanical strengthof cracked rocks with thermal treatment:Evolution of crack tortusity and fracture toughness KIC in heat treated Westerly. G., from Nasseri et al., 2007

Heat treated (RT, 250, 450, 650 & 850deg C, isotropic granite (WesterlyG.)


Elastic properties of cracked rocks: modelling using EMT

Assumption: wavelength << cracks ~ High Frequency (Fc~KHz)


Elastic properties of cracked rocks: modelling using EMT

and φ=ρ.ζ

O’Connell and Budiansky, 1974 Kuster and Toksoz,1974

Levin and Markov, 2004

Le Ravalec and Gueguen, 1996

Kachanov, 1994

(Walsh, 1965)


Elastic properties of cracked rocks:Percolation thresholds

and φ=ρ.ζ

O’Connell and Budiansky, 1974 Kuster and Toksoz,1974

Levin and Markov, 2004

Le Ravalec and Gueguen, 1996

Kachanov, 1994

(Walsh, 1965)

ρ∼0.1

ρ∼1ρ>>1

Gueguen and Palciauskas, 1994

ρ<0.1


MODELLING ELASTIC WAVE VELOCITIES using EMTnon-interactive theory (isolated penny shaped cracks)ISOTROPY

P, S and P/S ratios evolutions with crack density

Schubnel et al., Pageoph, 2006


CRACK DENSITY WITH PRESSURE

ASPECT RATIO WITH PRESSURE

Elastic properties of cracked rocks: inversion of elastic wavesEtna basalt (It.)

P and S wave evolutions with pressurein one basalt sample and fit using Kachanov 1994

From Benson et al., JGR 2006, Schubnel et al., Pageoph, 2006


Error contour map as a function of aspect ratio and crack density

Uniqueness of the solution – error map as a function of the crack density and the aspect ratio

Elastic properties of cracked rocks: inversion of elastic wavesEtna basalt (It.)



Mechanical Strength of cracked rocks : experimental observationsfrom Nasseri et al., IJRM, 2007


Mechanical Strength of cracked rocks : micromechanical modeling

so

from Nasseri et al., IJRM, 2007


Linking permeability to elastic properties:Permeability k of a cracked rock can be written (Guéguen and Dienes [1989]):

k = 2/15 f w2 ρ ζ with

Transport properties of cracked rocks : prediction from elastic waves


Application to Etna basalt (It.)

Transport properties of cracked rocks :Full inversion (P & S elastic wave velocities, Porosity and permeability)


Application to Heat treated Westerly G (US)

Transport properties of cracked rocks :Full inversion (P & S elastic wave velocities, Porosity and permeability)


Conclusions

CRACKED ROCKSEffective elastic properties can be predicted:

# of all EMT, only Extended DEM and NIC assymptotically fall to zero! Others surrestimate crackinteractions, and even for isotropic distribution, predict a fragmentation percolation threshold between 0.5 and 1, which is too small?

# Using EMT (here Kachanov (1994) non-interactive crack mode)l enables to evolutions of of Pand S waves in the dry and saturated regimes at HF (and up to orthorhombic crack distribution symmetry). Partial saturation (or saturation with fluid different than water, or mixed fluids) could be performed.

# Once matrix and fluid properties are known, inversion of elastic waves enables to quantifydamage in terms of crack density, aspect ratio (and preferential orientation of the crack distribution if anisotropic). It also enables to quantify the saturation relatively well.


Conclusions

Coupling EMT with percolation theory:# enables to predict permeability evolution with pressure in a straightforward wayfrom elastic wave velocity inversion, both in isotropically and anisotropically cracked (and porous rocks, talk of Phil Meredith).

Coupling EMT with linear fracture mechanics:# enables to predict the evolution of mechanical strength (in the isotropic case).

Coupling EMT with poroelasticity # enables to predict dispersion due to squirt flow and go back to low frequency elastic modulii.


poroelasticity in an anisotropic mediumdispersion due to local fluid flow (« squirt flow », Mavko and Nur [1975])

Discussion : dispersion due to squirt flow (HF and LF modulii)


Problems:# Permeability is scale dependent. Willlab. prediction ever be applicalble to thefield?Scale issues may be neglected if we onlylook at wave velocity variations

# frequency effects on elastic properties:We need to have more data ondispersion, i.e. at LF and HF in order tovalidate models and upscaling.

# Are stress interactions really changingthe problem?In static, maybe not?


Perspectives# extend to anisotropy

# low frequency moduli in the lab ! (fluid viscosity and permeabilitydependance of LF/HF cut-off frequency)

# temperature dependance of elastic moduli

# acoustic tomography


Thank you all for your attention!


MODELLING ELASTIC WAVE VELOCITIES using EMTnon-interactive theory (isolated penny shaped cracks)GENERALIZED FORM from Kachanov [1994]

Dryd/(1+d) ~ 1

Wetd ~ 0

Schubnel and Gueguen, JGR 2003


Nojima fault core samples

Elastic properties of cracked rocks: inversion of elastic wavesanisotropy – orthorhombic symmetry – Nojima fault granite (Ja.)


Simultaneous (double) inversion of wet and dry P&S data!measurements performed by Zamora et al. [1999]




Application to Takadani granite (Ja.)

Transport properties of anisotropically cracked rocks : prediction from elastic waves

Permeability k of a cracked rock can be written (Guéguen and Dienes [1989]):k = 2/15 f w2 ρ ζ

From Benson et al., JGR 2006


Does not work - Stress Interactions are vital!

Mechanical strength of anisotropically cracked rocks : prediction from elastic waves using crack density tensor?

From Nasseri et al., Pageoph, 2006


Mode I – linear crack – stress field perturbation


Stress interactions – general case


dispersion of P and S waves in the wet regime

P wave dispersion Sv wavedispersion

Discussion : dispersion due to squirt flow (HF and LF modulii)


Azimuth ~125°


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